Moment-Based Bregman Clustering for Latent Distributional Heterogeneity in Panel Data

This paper develops a method for identifying latent distributional heterogeneity in panel data. The method partitions each individual time series into blocks, estimates a local coefficient in each block, maps the local coefficients into a fixed finite-dimensional feature vector, and clusters individuals by a Bregman objective. The target is the finite-dimensional functional Ψ(Fg) = E[ψ(β0ib) | gi = g] of the latent group-specific coefficient distribution, rather than the full distribution Fg. We establish a population identification theorem under separation of these functionals, uniform consistency of the estimated feature vectors, consistency of the global Bregman clustering estimator, and consistent group-number selection under a shrinking penalty condition. A separate fixed-weight quadratic Bregman single-linkage estimator achieves exact recovery under a uniform radius–separation inequality. A label-transfer theorem shows that classification contamination smaller than the center-estimation scale preserves the oracle first-order distribution; exact recovery is a sufficient special case. General Bregman generators are treated through the identification and global-objective consistency results, while the pseudo-Huber specification is implemented as a nonquadratic Lloyd diagnostic. We also give a Gaussian–Hermite correction for nonlinear feature bias caused by block-level coefficient estimation. Monte Carlo experiments cover mean, variance, higher-moment, weak-separation, wrong-group-number, and contaminated-error designs. A synthetic economic illustration shows that moment-based clustering recovers latent firm types that have identical mean pass-through but different response risk and asymmetry. A chapter for a real-data empirical application is reserved and contains no fabricated results.